He served as an alternate deputy to the LIX Legislature of the Mexican Congress for the Federal District, and on October 28, 2004, he took the place of Jorge Ortiz Alvarado when he asked to resign.

[1] From 2007 to 2009, he was the director general of the Institute of Registral Functions of the State of Mexico, which oversees real estate and land transactions; from 2009 to 2011, he directed the Sistema de Radio y Televisión Mexiquense.

15 people were killed in the crash, but Murat and fellow politician Alfonso Navarrete Prida escaped with comparatively minor injuries.

[6] In December 2015, Murat Hinojosa left his position at the head of INFONAVIT to formally announce his candidacy for the PRI candidate for Governor of Oaxaca.

He was a candidate for governor for the "Juntos hacemos más" coalition, made up of the Revolucionario Institucional, Verde Ecologista de México and Nueva Alianza parties.